Theorems · Theorem · nonassociative algebras

LieIdeal.killingForm_eq

∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
  [Module.Free R L] [Module.Finite R L] [IsDomain R] [IsPrincipalIdealRing R],
  killingForm R ↥I = (killingForm R L).restrict (LieIdeal.toLieSubalgebra R L I).toSubmodule

Defined in: Mathlib.Algebra.Lie.TraceForm
Cited by: 1 results in Mathlib
Foundations: Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Free Module.Finite IsDomain IsPrincipalIdealRing

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
IsDomainstatement and proof · cited by 2,196
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032
Module.Freestatement and proof · cited by 597
LinearMap.BilinFormstatement · cited by 501
LieIdealstatement and proof · cited by 282
IsPrincipalIdealRingstatement and proof · cited by 131
LieSubalgebra.toSubmodulestatement · cited by 90
LieIdeal.toLieSubalgebrastatement · cited by 48
killingFormstatement · cited by 34

Cited by1

Results whose statement or proof uses this declaration.

LieDerivation.IsKilling.killingForm_restrict_range_adproof · cited by 2